Distance Measures in Multivariate Constrained Regression

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A problem of detecting influential observations in multivariate constrained regression is considered. Two types of distance measures are found. Cook s distance introduced in the ordinary univariate linear regression is adapted to multivariate regression with linear constraints on regression coefficients and its explicit form will be derived. Likelihood distances for multivariate constrained regression will be computed for two cases: one is the case in which both the regression coefficients and the covariance matrix are of interest and the other is the case in which only the regression coefficients are of interest. A numerical example is given for illustration.